Ockham and Induction

Ed of Beyond Necessity reports that he has translated some chapters on induction from Ockham's Summa Logicae. He goes on:

Ockham says that induction "is a progression from singulars to the universal", which is pretty much the modern understanding of the term.

That is not wrong, but it is not quite right either.  On a well-informed modern understanding induction need not involve "a progression from singulars to the universal."

Suppose that every F I have encountered thus far is a G, and that I conclude that the next F I will encounter will also be a G. This is clearly an inductive inference, but it is one that moves from a universal statement to a statement about an individual. The inference is from Every F thus far encountered is a G to The next F I will encounter will be a G.  So it is simply not the case that every inductive inference proceeds from singular cases to a universal conclusion. Some such inferences do, but not all.  This is a common misunderstanding.

It is also a mistake to think that deduction always proceeds from the universal to the singular.  See On Falsely Locating the Difference Between Deduction and Induction.

Comments

[Edward Ockham]

Hmm, I stand corrected. However, on the "next singular" counterexample, isn't there really an implicit universal middle here? I.e.

Every F thus far encountered is a G
[implicit]Every F is a G
Ergo, the next F I will encounter will be a G.

Meanwhile I have translated the next chapter and I now see where Ockham is coming from. He is worried about predestination.

That said, I haven't the faintest idea what is going on there. Does anyone else understand? Ockham is normally very clear, but I am struggling with this bit.

[Bill Vallicella]

Ed,

No doubt you have the Marilyn McCord Adams & Norman Kretzmann translation entitled Predestination, God's Foreknowledge, and Future Contingents. That includes copious notes which may be of help to you.

The argument you give above is an example of deduction, not induction. Or am I missing something?

[Edward Ockham]

>>No doubt you have the Marilyn McCord Adams & Norman Kretzmann translation entitled Predestination, God's Foreknowledge, and Future Contingents. That includes copious notes which may be of help to you.
<<

Actually I don't - predestination is not my thing, but I will have a look. Adams and Kretzmann are/were giants in the field of medieval philosophy.

>>The argument you give above is an example of deduction, not induction. Or am I missing something?
<<

Numbering the steps of the argument. Is the step from (1) to (2) deductive?

(1) Every F thus far encountered is a G
(2) Every F is a G
(3) Ergo, the next F I will encounter will be a G.

[Daniel K]

Maverick,
Why isn't the move from "Every F is a G" to "The next F I will encounter will be a G" a deduction? The inference from "Every F thus far encountered is a G" to "Every F is a G" would be the induction.

And if we generalize could we make a claim that all predictions are based on implicit universalizations?

If I sample from a bag of marbles and find that 75% of a good random sample are red and then make a prediction that the next marble will probably be red, haven't I implicitly first generalized something like "most of the marbles in the bar are red"?

If this was the case would it be fair to say that the inductive move is still from sample to generalization while deductive is a move from generalization to implications?

Thanks,
Daniel K.

[Bill Vallicella]

>>Why isn't the move from "Every F is a G" to "The next F I will encounter will be a G" a deduction?<<

Where did I say that it wasn't?

[Daniel K]

I must be misunderstanding. I was referring to this passage in your original post:
--------
On a well-informed modern understanding induction need not involve "a progression from singulars to the universal."

Suppose that every F I have encountered thus far is a G, and that I conclude that the next F I will encounter will also be a G. This is clearly an inductive inference, but it is one that moves from a universal statement to a statement about an individual.
--------
My claim was that the inference you describe relies on an implicit generalization that justifies the prediction.
P1 Every F I have encountered thus far is a G.
C1+P2 (Implicit) All Fs are Gs.
C2 (prediction) The next F I will encounter will also be a G

Another example:
P1 Every fire I have touched is hot.
C1+P2 (implicit) All fire is hot.
C2 (prediction) The next fire I will encounter will also be hot.

So, while you say the above inferences are inductive I wanted to say that they are not pure inductions. There is an inductive generalization and then a deductive implication that features as the prediction. There are really two inferences there instead of the one.

But the inductive generalization is in the move from P1 to C1. The prediction is an implication of the implicit generalization in C1.

Thanks,
Daniel

[Bill Vallicella]

Daniel,

You are reading too much into this. I was concerned in my post MERELY to show that my pal London Ed was wrong when he said that induction moves from singular statements to a universal statement.
At issue is what induction is, not the justification of induction.

Suppose a child examines seriatim a number of tomatoes. Each of them, he finds, is either red or orange. So he reasons, 'Every tomato looked at so far has been either red or orange; therefore the next one I encounter will be either red or orange.' That is an inductive inference if anything is, but it moves from a universal statement to a singular statement.

Roughly, what makes it inductive is that the conclusion goes beyond the information contained in the premise; in deduction, however, the conclusion merely explicates what is already contained in the premise(s).